# Group with Order Less than 60 is Solvable

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## Theorem

Every group whose order is less than $60$ is solvable.

## Proof

A direct consequence of Burnside's Theorem: the smallest number with $3$ distinct prime factors is $2 \times 3 \times 5 = 60$.

The validity of the material on this page is questionable.In particular: But $2 \times 3 \times 5 = 30$ not $60$. See talk page.You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by resolving the issues.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{Questionable}}` from the code.If you would welcome a second opinion as to whether your work is correct, add a call to `{{Proofread}}` the page. |

$\blacksquare$

## Sources

- 1971: Allan Clark:
*Elements of Abstract Algebra*... (previous) ... (next): Chapter $2$: Normal and Composition Series: $\S 75 \gamma$